Chapter 6 DEMAND

Demand Demand functions  the optimal amounts of each of the goods as a function of the prices and income faced by the consumer. Comparative statics  studying how demand responds to changes in the parameters (prices and income).

6.1 Normal and Inferior Goods Normal goods  the demand for the good would increase when income increases. x1x1 x2x2 Indifference curves Optimal choices Budget lines

6.1 Normal and Inferior Goods Inferior good  an increase of income results in a reduction in the consumption of the good. x1x1 x2x2 Indifference curves Budget lines Optimal choices

6.2 Income Offer Curves and Engel Curves Income offer curve: The locus of demanded bundles as the budget line shifts outward. Engel curve: demand for a good as a function of income, with prices fixed. x1x1 x1x1 x2x2 mIncome offer curve Indifference curves A Income offer curve Engel curve B Engel curve

6.3 Some Examples Perfect Substitutes  If p 1 <p 2, the consumer demands good 1 only, irrespective of income.  The demand for good 1 is x 1 =m/p 1, so the Engel curve is a straight line with a slope of p 1. x1x1 x1x1 mx2x2 Indifference curves Typical budget line Income offer curve Engel curve Slope=p 1

6.3 Some Examples Perfect Complements  The consumer demands the same amount of each good.  The demand for good 1 is x 1 =m/(p 1 +p 2 ), so the Engel curve is a straight line with a slope of p 1 +p 2. x1x1 x1x1 m x2x2 Indifference curves budget lines Engel curve Slope=p 1 +p 2 Income offer curve

6.3 Some Examples Cobb-Douglas Preference u(x 1,x 2 )=x 1 a x 2 1-a  Demand is x 1 =am/p 1, x 2 =(1-a)m/p 2.  The Engel curve for good 1 is a straight line with a slope of p 1 /a. x1x1 x1x1 x2x2 m Income offer curve Indifference curves Engel curve Slope=p 1 /a

6.3 Some Examples Homothetic Preferences x1x1 x1x1 x2x2 m Indifference curves Income offer curve Engel curve

6.3 Some Examples Quasilinear preferences u(x 1, x 2 )=v(x 1 )+x 2  Income offer curve is L-shaped.  Zero income effect for good 1 when income is sufficiently high. x1x1 mx2x2 Income offer curve Indifference curves Engel curve x1x1

6.4 Ordinary Goods and Giffen Goods An ordinary good  The demand for a good increases when its price decreases. x1x1 x2x2 Indifference curves Optimal choices

6.4 Ordinary Goods and Giffen Goods A Giffen good  The demand of a Giffen good decreases when its price decreases. x1x1 x2x2 Reduction in demand for good 1 Indifference curves

6.5 The Price Offer Curve and the Demand Curve price offer curve  The locus of demanded bundles as the price of one good changes. x1x1 x2x2 Indifference curves Price offer curve

6.5 The Price Offer Curve and the Demand Curve Demand curve:  The demand of a good expressed as a function of own price only.  We would normally have x1x1 p1p1 Demand curve

6.6 Some Examples Perfect Substitutes: The demand for good 1 is:  zero when p 1 >p 2  any amount on the budget line when p 1 =p 2  m/p 1 when p 1 <p 2 x1x1 x1x1 x2x2 p1p1 Indifference curves m/p 1 =m/p 2 * Demand curve p1=p2*p1=p2* Price offer curve

6.6 Some Examples Perfect Complements  The demand for good 1 is x 1 =m/(p 1 +p 2 ).  Fix m and p 2 and plot the relationship between x 1 and p 1. x1x1 x1x1 p1p1 x2x2 Demand curve Price offer curve Indifference curves

6.7 Substitutes and Complements Good 1 is a substitute for good 2 if △ x 1 / △ p 2 >0 Good 1 is complement to good 2 if △ x 1 / △ p 2 <0 It is possible that good 1 is a substitute (complement) for good 2, but the reverse is not true. Substitutes and complements are defined in terms of the Hicksian demand function.

6.8 The Inverse Demand Function Demand curve  x 1 as a function of p 1. Inverse demand curve  p 1 as a function of x 1. x1x1 Inverse demand curve p1p1